isi-entrance 2014 Q18

isi-entrance · India · solved Number Theory GCD, LCM, and Coprimality
Let $N$ be the smallest positive integer such that among any $N$ consecutive integers, at least one is coprime to $374 = 2 \times 11 \times 17$. Find $N$.
(A) 4 (B) 5 (C) 6 (D) 7
(C) $N = 6$
Let $N$ be the smallest positive integer such that among any $N$ consecutive integers, at least one is coprime to $374 = 2 \times 11 \times 17$. Find $N$.

(A) 4 \quad (B) 5 \quad (C) 6 \quad (D) 7